One day after leading Republicans to control of the Senate, incoming Majority Leader Mitch McConnell said Wednesday he hopes Congress can work with President Barack Obama on trade, taxes and other issues. But he said veto showdowns are also possible in the two-year era of divided government just ahead.

"There will be no government shutdown or default on the national debt," the Kentucky lawmaker pledged at a news conference, making clear he doesn't agree with some tea party-backed lawmakers who have supported one or the other in the past — or may want to in the future.

McConnell, famously taciturn, smiled and joked with reporters one day after the fulfillment of a lifelong dream.

He will take office in January as Senate majority leader, and he and House Speaker John Boehner will have the authority to set the congressional agenda.

Obama, at the White House, arranged to field questions from reporters later in the day.

The events unfolded as jubilant Republicans celebrated sweeping election gains that left them in control of the Senate for the first time since 2006, near a post-World War II high in House seats and in possession of governorships in a handful of states that had been held by Democrats.

"We won in red states, we won in blue states and we won in purple states," said Republican chairman Reince Priebus, calling the returns a rejection of Obama's policies.

Boehner ceded the Republican limelight to McConnell for the day. The Ohio Republican is in line for a third term as House leader — and his first with a Republican majority in the Senate.

At his news conference, McConnell said that "in our system the president is the most important player" who can veto legislation or persuade lawmakers of his own party to back compromise.

"When America chooses divided government, I don't think it means they don't want us to do anything. It means they want to do things for the country," he said.

He cited trade legislation and an overhaul of the tax rules as two areas ripe for agreement.

Beyond that, he made it clear Congress will vote on legislation to approve the Keystone XL oil pipeline from Canada through the United States, and work to repeal portions of the health care law that stands as Obama's signature domestic accomplishment. He said a tax on medical devices and a mandate for individuals to purchase health insurance are also Republican targets. Congress will hold hearings on the IRS, he said.

Republicans are also expected to mount a major attack on federal deficits.

Rep. Steve Israel of New York, in charge of the Democrats' House campaign operations, said the election returns could have been worse. They were bad enough for the president's party.

Republicans were assured of a gain of seven Senate seats, and they bid for another in Alaska, where the vote count was not complete. Also uncalled was a race in Virginia, where Democratic Sen. Mark Warner faced challenger Ed Gillespie.

Also in doubt was a Senate seat in Louisiana, where Rep. Bill Cassidy led Democratic Sen. Mary Landrieu into a Dec. 6 runoff.

Despite the reverses, Sen. Harry Reid of Nevada announced he intended to remain as the Democratic leader. There was no sign of opposition.

In the House, Republicans were within hailing distance of their largest majority since World War II, 246 seats in 1946, when Harry Truman sat in the White House.

There was no word whether Rep. Nancy Pelosi, D-Calif., would seek another term as leader.

Already, the jockeying was underway for the next election, one to pick a president in 2016.

New Jersey Gov. Chris Christie and Sen. Rand Paul of Kentucky, both Republican hopefuls, were up early for morning television appearances.

Exit polls show the GOP drew strength from voters who felt left behind economically. Almost half said their own families' financial situations hadn't improved much over the past two years, and a fourth said it had gotten worse. Those who said their finances were worse supported Republican congressional candidates by more than a 2-1 margin.

Even as they turned against Obama and Democrats, voters also expressed scant confidence in Republican leaders, underscoring the increased pressure that Republicans will face to deliver next year when they control both houses of Congress.

Outside groups were standing ready with millions in advertising time for the Louisiana runoff. The Koch-backed Freedom Partners Action Fund had reserved more than $2 million in airtime, starting with ads that Louisiana voters were to begin seeing on Wednesday. The Senate Republicans' campaign arm had booked $2.8 million in ads and the Senate Democrats' committee already had planned $1.8 million in ads.

In state capitols, Republicans picked up governors' seats in reliably Democratic states like Illinois, Maryland and Massachusetts. With Congress grappling with gridlock, states have been at the forefront of efforts to raise the minimum wage and implement Obama's health care law.